If the points P,Q,R,S are (4,7,8),(-1,-2,1),(2,3,4) and (1,2,5)` respectively show that PQ and RS intersect. Also find the point of intersection.

If P,Q,R,S are (3,6,4),(2,5,2),(6,4,4,),(0,2,1) respectively find the projection of PQ on RS.

If coordinates of P,Q,R,S and (3,6,4),(2,5,2),(6,4,4),(0,2,1) respectively, find the projection of PQ on RS.

The points P(3,2,4), Q(4,5,2), R(5,8,0) and S(2,-1,6) are

A (4,8), B(5,5), C(2,4) and D (1,7) are the vertices of the parallelogram . Find the coordinates of the point of intersection of its diagonals .

The point P (3,2,4),Q(4,52),R(5,8,0) and S(2,-1,6) are :

Find the ratio in which the line segment, joining the points, P(2,3,4) and Q(-3,5,-4) is divided by the yz-plane. Also, find the points of intersection.

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

If coordinates of point P,Q,R,S are respectively (6,3,2);(5,1,4);(3,4,-7) and (0,2,5) then the projection of PQ on RS are

P,Q,R,S are the points (1,2,-2), (8,10,11), (1,2,3) and (3,5,7) respectively. If s denotes the projection of PQ on RS then 29s^(2) + 29 is equal to :